5.1 Homework

1. Fill in each blank with the appropriate word or phrase.  If an event is certain to occur, its probability is  _____. An outcome or collection of outcomes from a sample space is called  ________

2.  Assume that a fair die is rolled. The sample space is 

, and all the outcomes are equally likely. Find P (Even number). Express your answer in exact form.

P(Even Number) =

3.  Assume that a fair die is rolled. The sample space is 

, and all the outcomes are equally likely. Find P(less than 4).  . Write your answer as a fraction or whole number.

P(Less than 4) =

4.  A coin flip: A fair coin is tossed three times. The outcomes of the three tosses are recorded. Round your answers to four decimal places if necessary.

A. Assuming the outcomes to be equally likely, find the probability that all three tosses are “Heads.”

The probablility that all three tosses are “Heads” is  _________

B. Assuming the outcomes to be equally likely, find the probability that the tosses are all the same.

The probablility that the tosses are the same is ________.

C. Assuming the outcomes to be equally likely, find the probability that exactly two of the three tosses is “Tails.”

The probablility that exactly two of the three tosses is “Tails” is __________.

5.   Pitching: During a recent season, pitcher Clayton Kershaw threw 2526 pitches. Of these,  1263 were fastballs, 25 were changeups, 379 were curveballs, and  859 were sliders. Round the answers to four decimal places as needed.

(a)What is the probability that Clayton Kershaw throws a fastball?
(b)What is the probability that Clayton Kershaw throws a breaking ball (curveball or slider)?

The probability that Clayton Kershaw throws a fastball is  _______.

The probability that Clayton Kershaw throws a breaking ball (curveball or slider) is ________.

6.   Risky drivers: An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,199 customers,  7782 are good risks,  2477 are medium risks, and 940 are poor risks. As part of an audit, one customer is chosen at random. Round your answers to four decimal places if necessary.

(a) What is the probability that the customer is a good risk?

The probability that the customer is a good risk is ___________.

(b) What is the probability that the customer is not a poor risk?

The probability that the customer is not a poor risk is ______.

7.   Roulette: A Nevada roulette wheel has 38 pockets. Eighteen of them are red, eighteen are black, and two are green. Each time the wheel is spun, a ball lands in one of the pockets, and each pocket is equally likely.

(a) What is the probability that the ball lands in a green pocket? Round your answer to four decimal places.

The probability that the ball lands in a green pocket is _______.

(b) If you bet on green on every spin of the wheel, you will lose more than 90% of the time in the long run. Explain why this is so. Round your answer to two decimal places.

You will lose more than 90% of the time in the long run if you always bet on green because _________   says that in the long run, the percentage of the time you lose will approach  _______ %.

8. Hospital visits: According to a health agency, there were  409,706 hosital visits for asthma–related illnesses in a recent year. The age distribution was as follows. Round your answers to four decimal places if necessary.

(a) What is the probability that an asthma patient is between 45 and 76 years old?

The probability that an asthma patient is between  45 and 76 years old is ________.

(b) What is the probability than an asthma patient is 85 years old or older?

The probability that an asthma patient is  85 years old or older is __________.

(c) Using a cutoff of 0.05 , is it unusual for an asthma patient to be less than 1 year old?

Based on a cutoff of 0.05 , it _____ unusual for an asthma patient to be less than  1 year old.